Game Studio: Scores at Scale

Estimate large and small quantities, then compare their sizes.

Build the Estimates

A video game studio is checking its level designs. Round each quantity to one significant digit: a whole-number digit from 1 through 9 times a power of 10.

A test server recorded 47,200,000 points. Which is the required estimate?

A. 4 × 10⁷ pointsB. 5 × 10⁶ pointsC. 5 × 10⁸ pointsD. 5 × 10⁷ points

The probability of earning a rare bonus on one attempt is 0.0000063. Which is the required estimate?

A. 6 × 10⁶B. 7 × 10⁻⁶C. 6 × 10⁻⁶D. 6 × 10⁻⁵

Players earned 823,000,000 points during a weekend test. Complete the required estimate.

× 10⁸ points

A game engine operation takes 0.000000374 seconds. Its one-significant-digit estimate is 4 × 10ⁿ seconds. Find n.

n =

A season's total is 98,000,000 points. Which estimate follows the required form after rounding?

A. 1 × 10⁸ pointsB. 9 × 10⁸ pointsC. 9 × 10⁷ pointsD. 1 × 10⁷ points

Compare the Scales

When exact quantities are given, first round each to one significant digit. Use those estimates to find each comparison factor.

The studio compares two level jackpots.

Level Jackpots
Level	Points
Citadel	6,200,000
Outpost	310,000

Using the rounded estimates, the Citadel jackpot is times as large as the Outpost jackpot.

A silver reward has probability 0.000081 per attempt. A crystal reward has probability 0.000000041 per attempt. Estimate each probability first.

The estimated silver reward probability is times as large as the estimated crystal reward probability.

Two estimated score totals are 7 × 10⁹ points and 7 × 10⁶ points. How many times as large is the greater total?

A. 1,000 times as largeB. 3 times as largeC. 100 times as largeD. 7,000 times as large

Select every pair in which the first estimated quantity is 100 times as large as the second.

10.

A basic achievement is worth about 4 × 10⁴ points. A final achievement is worth 1,000 times as many points. Write the final achievement's estimated value as 4 × 10ⁿ points.

n =

Make Balance Decisions

Use one-significant-digit estimates to make each decision. Show your reasoning for the final question.

11.

A level needs a bonus worth at least 100 times its estimated base reward. Round both values before deciding whether this bonus qualifies.

Proposed Reward Balance
Reward	Points
Base	42,000
Bonus	3,700,000

A. It qualifies; the estimated factor is 10.B. It qualifies; the estimated factor is 100.C. It does not qualify; the estimated factor is 100.D. It does not qualify; the estimated factor is 10.

12.

A new mode should award about 400 times the points of a practice mode. The practice mode awards an estimated 2 × 10⁵ points. Express the new mode's target as a single digit times a power of 10.

Target: × 10ⁿ points, where n =

13.

A score-checking routine originally took 0.00072 seconds. An updated routine takes 0.00024 seconds. First round each time to one significant digit. Use the rounded values, not the original values, for your comparison.

The estimated original time is times as large as the estimated updated time.

14.

Two bonus chances are estimated as 2 × 10⁻³ and 8 × 10⁻⁵. Eli says, “The first chance is 100 times as large because the exponents differ by 2.” Explain what Eli overlooked and find the correct comparison factor.